CHAPTER 11. LIFE-CYCLE COST SUBGROUP ANALYSIS

TABLE OF CONTENTS

11.1 INTRODUCTION.............................................................................................................. 11-1

11.2 SUB-GROUPS DEFINITION .......................................................................................... 11-1

11.2.1 Commercial Customer Sub-Group ....................................................................... 11-1

11.2.2 Small Business Commercial Discount Rate......................................................... 11-1

11.2.3 Life-Cycle Cost and Payback Period Results for Small Business SubGroup...................................................................................................................... 11-2

LIST OF TABLES

Table 11.2.1 Discount Rate Difference between Small Company and Sector 

Average ............................................................................................................ 11-2

Table 11.2.2 PTAC 9,000 Btu/h Units: LCC Results Comparison between Small 

Business and Sub-Group and All Buildings.................................................. 11-3

Table 11.2.3 PTAC 15,000 Btu/h Units: LCC Results Comparison Between Small 

Business and Sub-Group and All Buildings.................................................. 11-3

Table 11.2.4 PTHP 9,000 Btu/h Units: LCC Results Comparison Between Small 

Business and Sub-Group and All Buildings.................................................. 11-4

Table 11.2.5 PTHP 15,000 Btu/h Units: LCC Results Comparison Between Small 

Business and Sub-Group and All Buildings.................................................. 11-4

Table 11.2.6 PTAC 9,000 Btu/h Units: PBP Results Comparison Between Small 

Business Sub-Group and All Buildings......................................................... 11-5

Table 11.2.7 PTAC 15,000 Btu/h Units: PBP Results Comparison Between Small 

Business Sub-Group and All Buildings......................................................... 11-5

Table 11.2.8 PTHP 9,000 Btu/h Units: PBP Results Comparison Between Small 

Business Sub-Group and All Buildings......................................................... 11-6

Table 11.2.9 PTHP 15,000 Btu/h Units: PBP Results Comparison Between Small 

Business Sub-Group and All Buildings......................................................... 11-6

11-i 
CHAPTER 11. LIFE-CYCLE COST SUBGROUP ANALYSIS

11.1 INTRODUCTION

The life-cycle cost (LCC) sub-group analysis evaluates impacts on any identifiable 

groups of commercial customers of packaged terminal air conditioners (PTACs) and packaged 

terminal heat pumps (PTHPs) who may be disproportionately affected by a national energyefficiency standard. The U.S. Department of Energy (DOE) accomplished this, in part, by 

analyzing the LCC and payback period (PBPs) for those commercial customers that fall into 

specific sub-groups.

DOE determined the impact on commercial customer sub-groups using the LCC 

spreadsheet model. The standard LCC and PBP analysis (described in Chapter 8) includes 

various types of commercial buildings that use PTAC equipment. The LCC spreadsheet model 

allows for the identification of certain sub-groups of commercial customers that can then be 

analyzed by sampling only that sub-group. (Chapter 8 explains in detail the inputs to the 

spreadsheet model used in determining the LCC and PBP.)

This chapter describes the subgroup identification in further detail and gives the results of 

the LCC and PBP analysis for the considered subgroups. 

11.2 SUB-GROUPS DEFINITION

11.2.1 Commercial Customer Sub-Group

DOE identified small businesses as a sub-group that possibly could be disproportionately 

affected by PTAC efficiency standards. DOE was concerned that increases in the purchase price 

of equipment could have negative impacts on small businesses (i.e., those with low annual 

revenues). 

The U.S. Small Business Administration (SBA) established size standards to define small 

businesses for types of economic activity, or industry, under the North American Industry 

Classification System (NAICS)1

. The SBA defines a small business by either its annual receipts 

(i.e., revenues) or its number of employees. In the case of traveler accommodations, firms with 

annual revenues of $7 million or less are categorized as small businesses. Generally, chain hotels 

do not meet this criterion, but a substantial portion of independent hotels do. Based on data 

reported by Ducker Worldwide, DOE established that independent hotels are the primary small

business subgroup, representing approximately 10% of the total building sample. 2

11.2.2 Small Business Commercial Discount Rate

The capital asset pricing model (CAPM) underestimates the cost of capital for small 

companies. In CAPM, the risk premium β is used to account for the higher returns associated 

with greater risk. However, for small companies, particularly very small companies, historic 

11-1 
returns have been significantly higher than the CAPM equation predicts. This additional return 

can be accounted for by adding a size premium to the cost of equity for small firms:

Rk ( ) ERP S fe β +×+=

Where:

ke = cost of equity,

Rf = expected return on risk-free assets,

β = risk coefficient of the firm, 

ERP = equity risk premium, and

S = size premium.

DOE obtained size premium data from Ibbotson Associates’ Stocks, Bonds, Bills, and 

Inflation 2009 Yearbook.

3

 For the period of 1926-2008, the average size premium for the smallest 

companies in all industries is 5.81%, implying that on average, historic performance of small 

companies has been 5.81% higher than the CAPM estimate of the small company cost of equity.

a

DOE calculated the real weighted-average cost of capital (as described in Chapter 8) 

using the cost of equity including a size premium for small companies instead of the CAPM cost 

of equity.4

 Table 11.2.1 presents DOE’s estimates of the discount rates for entire sectors, small 

companies specifically, and the small company discount rate premium. 

To estimate the impact of standards specifically on small businesses, the small company 

discount rates for each sector were used in the LCC and PBP analysis instead of the sector 

average discount rates. 

Table 11.2.1 Discount Rate Difference between Small Company and Sector Average 

Hotels

Discount Rate

Average Standard

Deviation

Small Company 

Discount Rate Premium

Entire Sector 6.31% 2.03%

1.52% 

Small Companies 7.83% 3.12%

11.2.3 Life-Cycle Cost and Payback Period Results for Small Business Sub-Group

Table 11.2.2 to Table 11.2.5 summarize the LCC results for the small business sub-group 

for each of the PTAC and PTHP equipment classes, and compare them to the results for the total 

sample of buildings used in the overall LCC analysis. Table 11.2.6 to Table 11.2.9 summarize 

a In this calculation, small companies are defined as companies with market capitalization of less than or equal to 

$218.53 million, the Ibbotson Associates’ definition of Decile 10 companies. 

11-2 

 
the PBP results. Results are provided by trial standard level (TSL). Note that this is likely an 

overestimate of the impact on small businesses; not all independent hotels qualify as small 

businesses. 

As is evident from the LCC and PBP results, the effect of higher PTAC and PTHP

standards on small businesses is similar to the effect on the full sample of commercial customers. 

Thus, small businesses are not substantially disadvantaged by increased PTAC and PTHP 

equipment standards, as compared to the general population of commercial customers.

Table 11.2.2 PTAC 9,000 Btu/h Units: LCC Results Comparison between Small Business 

and Sub-Group and All Buildings

TSL EER

Small Businesses All Buildings

Mean 

LCC

Mean Increase 

in LCC from 

Baseline

Percent of 

Units with 

LCC Savings 

Mean 

LCC

Mean Increase 

in LCC from 

Baseline

Percent of 

Units with 

LCC Savings 

Baseline 11.1 $2,493 - - $2,586 - -

ASHRAE 11.3 $2,494 $1 22% $2,587 $1 30%

1 11.5 $2,501 $8 8% $2,593 $7 11% 

2 12.0 $2,506 $13 10% $2,597 $11 14%

3 12.4 $2,512 $19 11% $2,602 $16 16%

4 12.9 $2,520 $27 10% $2,609 $23 13% 

5 13.1 $2,525 $32 9% $2,614 $27 12% 

Table 11.2.3 PTAC 15,000 Btu/h Units: LCC Results Comparison Between Small Business 

and Sub-Group and All Buildings

EL EER

Small Businesses All Buildings

Mean 

LCC

Mean Increase 

in LCC from 

Baseline

Percent of 

Units with 

LCC Savings 

Mean 

LCC

Mean Increase 

in LCC from 

Baseline

Percent of 

Units with 

LCC Savings 

Baseline 9.3 $3,070 - - $3,192 - -

ASHRAE 9.5 $3,070 $0 38% $3,191 $0 49% 

1 9.7 $3,078 $8 5% $3,198 $6 7%

2 10.0 $3,088 $17 4% $3,207 $15 6%

3 10.4 $3,105 $35 2% $3,223 $32 3%

4 10.8 $3,130 $60 1% $3,247 $56 1% 

5 11.0 $3,146 $76 1% $3,262 $71 1% 

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Table 11.2.4 PTHP 9,000 Btu/h Units: LCC Results Comparison Between Small Business 

and Sub-Group and All Buildings

EL EER

Small Businesses All Buildings

Mean 

LCC

Mean 

Decrease in 

LCC from 

Baseline* 

Percent of 

Units with 

LCC 

Savings 

Mean 

LCC

Mean 

Increase/(Decrease) in 

LCC from Baseline* 

Percent of 

Units with 

LCC 

Savings 

Baseline/

ASHRAE 11.3 $3,144.1 - - $3,284 - - 

1 11.5 $3,138.4 ($6) 43% $3,277 ($7) 45%

2 12.0 $3,137.8 ($6) 37% $3,275 ($2) 42% 

3 12.4 $3,138.8 ($5) 41% $3,274 ($1) 50%

4 12.9 $3,141.3 ($3) 39% $3,275 $1 48% 

5 13.1 $3,143.2 ($1) 36% $3,276 $1 46%

* Parentheses indicated negative values

Table 11.2.5 PTHP 15,000 Btu/h Units: LCC Results Comparison Between Small Business 

and Sub-Group and All Buildings

EL EER

Small Businesses All Buildings

Mean 

LCC

Mean 

Increase/(Decrease) 

in LCC from 

Baseline* 

Percent 

of Units 

with 

LCC 

Savings 

Mean 

LCC

Mean 

Increase/(Decrease) 

in LCC from 

Baseline* 

Percent 

of Units 

with 

LCC 

Savings 

Baseline/

ASHRAE 9.5 $3,853.5 - - $4,033 - - 

1 9.7 $3,853.5 ($0) 24% $4,032 ($1) 30% 

2 10.0 $3,852.6 ($1) 25% $4,030 ($4) 31%

3 10.4 $3,859.5 $6 24% $4,034 $1 31%

4 10.8 $3,873.9 $20 16% $4,047 $14 22%

5 11.0 $3,884.0 $31 13% $4,056 $23 18% 

* Parentheses indicated negative values

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Table 11.2.6 PTAC 9,000 Btu/h Units: PBP Results Comparison Between Small Business 

Sub-Group and All Buildings

EL EER

Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

ASHRAE 11.3 8.8 8.8 8.8 8.8

1 11.5 9.3 9.4 9.3 9.4 

2 12.0 9.9 9.9 9.9 9.9

3 12.4 10.6 10.6 10.6 10.6

4 12.9 11.1 11.2 11.1 11.2 

5 13.1 11.4 11.5 11.4 11.5 

Table 11.2.7 PTAC 15,000 Btu/h Units: PBP Results Comparison Between Small Business 

Sub-Group and All Buildings

EL EER

Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

ASHRAE 9.5 7.3 7.4 7.3 7.4

1 9.7 9.3 9.4 9.3 9.4 

2 10.0 12.0 12.3 12.0 12.3

3 10.4 15.6 15.7 15.6 15.7 

4 10.8 18.4 18.7 18.4 18.7 

5 11.0 20.1 20.3 20.1 20.3 

11-5 
Table 11.2.8 PTHP 9,000 Btu/h Units: PBP Results Comparison Between Small Business 

Sub-Group and All Buildings

TSL EER

Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

1 11.3 4.3 4.4 4.3 4.4

2 11.5 5.9 5.8 5.9 5.8 

3 12.0 6.8 6.9 6.8 6.9

4 12.4 7.4 7.5 7.4 7.5 

5 12.9 7.5 7.7 7.5 7.7

Table 11.2.9 PTHP 15,000 Btu/h Units: PBP Results Comparison Between Small Business 

Sub-Group and All Buildings

TSL EER

Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

1 9.7 7.1 7.2 7.1 7.2

2 10.0 6.9 7.0 6.9 7.0

3 10.4 8.4 8.5 8.4 8.5

4 10.8 9.8 10.0 9.8 10.0

5 11.0 10.4 10.6 10.4 10.6

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REFERENCES 

1. Title 13, Code of Federal Regulations, Chapter I-Small Business Administration, Part 

121-Small Business Administration, Subpart A-Size Eligibility Provisions and Standards. 

2005. 

2. Ducker Worldwide, 2000 U.S. Market for Residential and Specialty Air Conditioning: 

PTAC (Packaged Terminal Air Conditioning), March 2001. Ducker Industrial Standards. 

Bloomfield Hills, Michigan 48301. 

<http://www1.eere.energy.gov/buildings/appliance_standards/commercial/pdfs/ptac_pthp

_tsd/chapter_10.pdf> 

3. Ibbotson Associates, SBBI Valuation Edition 2009 Yearbook. 2009. Chicago, IL.

4. Damodaran Online, The Data Page: Cost of Capital by Industry Sector.

2012<http://pages.stern.nyu.edu/~adamodar> 

11-7